SOLUTION: what rational expression divided by 3a over 4 equals 1 over three

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Question 77989This question is from textbook algebra 1 a process approach
: what rational expression divided by 3a over 4 equals 1 over three This question is from textbook algebra 1 a process approach

Found 2 solutions by Edwin McCravy, stanbon:
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!

what rational expression divided by 3a over 4 equals 1 over three

Let the rational expression be R

Then R divided by 3a over 4 equals 1 over three

     R ÷ %283a%29%2F4 = 1%2F3
          
Put the R over 1

     R%2F1 ÷ %283a%29%2F4 = 1%2F3

Invert the %283a%29%2F4 and change the ÷ to ×

     R%2F1 × 4%2F%283a%29 = 1%2F3

Multiply numerators and denominators on the left:

     %284R%29%2F%283a%29 = 1%2F3

Multiply both sides by the LCD, %28%283a%29%2F1%29

     %28%283a%29%2F1%29%284R%29%2F%283a%29 = %28%283a%29%2F1%291%2F3

The 3a's cancel on the left, leaving just 4R
The 3's cancel on the right, leaving just a.

          4R = a

Divide both sides by 4:

          R=a%2F4

That's the rational expression.

Let's check and see:

     R ÷ %283a%29%2F4 = 1%2F3

   a%2F4 ÷ %283a%29%2F4 = 1%2F3

Invert the second fraction on the left and change the ÷ to ×:

   a%2F4 × 4%2F%283a%29 = 1%2F3

The 4's  and the a's cancel on the left, leaving 
just 1%2F3

                  1%2F3 = 1%2F3

So it checks.

Edwin

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
what rational expression divided by 3a over 4 equals 1 over three
x/(3a/4)= = 1
x=4/3a
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Cheers,
Stan H.